An LTI system is described by the difference equation y[n]=2x[n]=3x[n=1]+2x[n -2] (a) Draw the implementation of this system as a block diagram in direct form (b) Give the implementation as a block diagram in transposed direct form.

Step-by-step explanation:

What was Matthew's score?

If all of the 720 pairs of shoes are sold at $25.00 per pair with a profit margin of 25%, the shoe store will make $4,500.00.

Selling price is the amount of money that a seller charges for a particular product or service in order to make a profit.

The selling price of a pair of shoes is $25.00, and the profit for the shoe store is 25% of the selling price, or 0.25 x $25.00 = $6.25.

To find out how much the shoe store will make if all of the shoes are sold, we need to multiply the number of pairs of shoes by the selling price and then by the profit margin:

Total revenue = Number of pairs of shoes x Selling price x Profit margin

Total revenue = 720 pairs x $25.00 x 0.25

Total revenue = $4,500.00

Therefore, if all of the 720 pairs of shoes are sold at $25.00 per pair with a profit margin of 25%, the shoe store will make $4,500.00.

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The cost of constructing the box will be = $81.77

Since the question gives us information about the rectangle,

so the area of the rectangle is shown by,

Area = 2 x (length + width)

So we have the area as,

Area = 2(lh + wh) +lw

(since the area per square meter is also given so we added l x w)

Since the cost of the base is = $5 per square meter and the cost of the sides is = $3 per square meter, so area in terms of the cost function,

⇒ C = 3 x 2(lh + wh) + 5 x l x w

⇒ C = 6(lh + wh) +5lw ---------equation 1

According to the question, the length of the rectangular container is twice that of the width of the container,

⇒ l = 2w

Substituting the new value of l in equation 1,

⇒ C = 6(2wh + wh) + 10 \(w^{2}\)

⇒ C = 18wh + 10 \(w^{2}\) ---------- equation 2

To calculate the volume of the rectangle,

V = length x width x height ( lwh )

substituting v = 10 and 2w = l,

2\(w^{2}\)h = 10

h = \(\frac{5}{w^{2} }\)

Substitute the value of h in equation 2,

⇒ C = 18w x \(\frac{5}{w^{2} }\) + 10\(w^{2}\)

⇒ C = \(\frac{90}{w}\) + 10\(w^{2}\) --------- equation 3

Differentiating the above equation we get,

⇒ C* = - \(\frac{90}{w^{2} }\) + 20w

⇒ 20w = \(\frac{90}{w^{2} }\)

Multiply both sides by \(w^{3}\)

⇒ \(20w^{3}\) = 90

⇒ \(w^{3}\) = 4.5

w = 1.65

Put the value of w in equation 3,

⇒ C = \(\frac{90}{1.65}\) + 10 x \(1.65^{2}\)

⇒ C = 81.77

Therefore, The cost of constructing the box will be = $81.77

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Answer:

20 years

Step-by-step explanation:

Given the ratio of their ages = 5 : 4 = 5x : 4x ( x is a multiplier )

Then in 5 years

5x + 5 : 4x + 5 = 6 : 5 , that is

\(\frac{5x+5}{4x+5}\) = \(\frac{6}{5}\) ( cross- multiply )

5(5x + 5) = 6(4x + 5) ← distribute parenthesis on both sides

25x + 25 = 24x + 30 ( subtract 24x from both sides )

x + 25 = 30 ( subtract 25 from both sides )

x = 5

Thus

Kiran's age is 4x = 4 × 5 = 20

The trend projection for time period 18 is 197.6. The correct option is B

A mathematical equation used to represent the trend or pattern seen in a time series of data is called a linear trend expression, sometimes referred to as a linear trend model.

To find the trend projection for time period 18 using the given linear trend expression, we substitute t = 18 into the equation:

Yt = 129.2 + 3.8t

Y18 = 129.2 + 3.8 * 18

Y18 = 129.2 + 68.4

Y18 = 197.6

Therefore, the trend projection for time period 18 is 197.6.

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Answer:

Step-by-step explanation:

19?

Answer:

5 km

Step-by-step explanation:

Answer:

\(\dfrac{3x-1}{2x^2-3x}\)

Step-by-step explanation:

Given rational expression:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}\)

First, we need to eliminate the negative exponent in the numerator.

To do this, multiply the numerator by x / x:

\(\begin{aligned}(x^{-1}+3x-4) \cdot \dfrac{x}{x}&=\dfrac{ x^{-1}\cdot x+3x\cdot x-4 \cdot x}{x}\\\\&=\dfrac{1+3x^2-4x}{x}\end{aligned}\)

Therefore:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}=\dfrac{\frac{1+3x^2-4x}{x}}{2x^2-5x+3}\)

\(\textsf{Apply\:the\:fraction\:rule:}\:\dfrac{\frac{a}{b}}{c}=\dfrac{a}{b\cdot \:c}\)

                       \(=\dfrac{1+3x^2-4x}{x\cdot (2x^2-5x+3)}\)

                       \(=\dfrac{3x^2-4x+1}{x(2x^2-5x+3)}\)

Factor the quadratics in the numerator and the denominator:

\(\begin{aligned}\textsf{Numerator:}\quad 3x^2-4x+1&=3x^2-3x-x+1\\&=3x(x-1)-1(x-1)\\&=(3x-1)(x-1)\end{aligned}\)

\(\begin{aligned}\textsf{Denominator:}\quad 2x^2-5x+3&=2x^2-2x-3x+3\\&=2x(x-1)-3(x-1)\\&=(2x-3)(x-1)\end{aligned}\)

Therefore:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}=\dfrac{(3x-1)(x-1)}{x(2x-3)(x-1)}\)

Factor out the common term (x - 1):

                      \(=\dfrac{3x-1}{x(2x-3)}\)

Simplify the denominator:

                      \(=\dfrac{3x-1}{2x^2-3x}\)

Therefore:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}=\boxed{\dfrac{3x-1}{2x^2-3x}}\)

We have two solutions for x: x = 5 and x = 2 So, the points on the curve where the tangent is horizontal have x-values of x = 5 and x = 2.  the points on the curve where the tangent is horizontal are (2, 13.3333) and (5, 26.6667).

To find the points on the curve where the tangent is horizontal, we need to find where the derivative of the curve is equal to zero. Taking the derivative of y = 1/3 x³ – 3.5x² + 10x + 14, we get:

y' = x² - 7x + 10

Setting y' equal to zero and solving for x, we get:

x² - 7x + 10 = 0

Factoring, we get:

(x - 2)(x - 5) = 0

So the x-values where the tangent is horizontal are x = 2 and x = 5. To find the corresponding y-values, we can plug these values back into the original equation:

y(2) = 1/3(2)³ – 3.5(2)² + 10(2) + 14 = 13.3333
y(5) = 1/3(5)³ – 3.5(5)² + 10(5) + 14 = 26.6667

Therefore, the points on the curve where the tangent is horizontal are (2, 13.3333) and (5, 26.6667).

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Answer:

The (a + b)2 formula is the algebraic identity used to find the square of the sum of two numbers.

Step-by-step explanation:

To find the formula of the binomial in the form (a + b)2, we will just multiply (a + b) (a + b).

Answer:

a^2b^3

Step-by-step explanation:

Expression:

ab^2(ab)

Simplify it:

a*a=a^2

b^2*b=b^3

Put them together:

a^2b^3

Hope this helps. Have a great day!

Answer:

$46.54

Step-by-step explanation:

A=P(1+r/n)^nt

P=220

r=.0325

n=1

t=6

A=266.54

A=P+I

266.54=220+I

I=46.54

Answer:

8.50f + 3.00h = 24

Step-by-step explanation:

The length of square B is 12 cm.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, square A is 3 cm long.

The scale that maps square A onto square B is 1:4.

Let the length of square B be x.

1/4 =3/x

x=4×3

x=12 cm

Therefore, the length of square B is 12 cm.

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Answer:

where r the graphs i can not help if u don't put the graphs

Step-by-step explanation:

Answer: 926

Step-by-step explanation:

1. 920- 444= 476

2. 476+450= 926

3. 926

Answer:926

Step-by-step explanation:because 920 - 444 = 476 + 450 = 926

The value of the gauge needle is, 9.01 cm

Given that;

The fuel gauge of a car represents how much gasoline is left in the tank. If the area of the sector represented by the fuel gauge is 10.6 square centimeters.

Now, We can formulate;

A = θ/360 πr

10.6 = (135/360) 3.14 x r

3816 = 423.5r

r = 9.01

Thus, The value of the gauge needle is, 9.01 cm

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Answer: 3:4 , 6:8 , and 18:24

Step-by-step explanation: To find the equivalent ratio: we should set up a proportional relationship:

\(\frac{6}{?}\) = \(\frac{3}{4}\)

3 x 2 = 6, so 4 x 2 would equal 8.

We can check by reducing 6/8 by 2 to get 3/4.

We do the same for the last one:

\(\frac{?}{24}\) =    \(\frac{3}{4}\)

4 x 6 = 24, so 3 x 6 = 18

So we can check if we are right by reducing. 18/24 divided by 6 = 3/4, so we are correct.

Answer:

108

Step-by-step explanation:

To find the volume of a rectangular prisms just multiply its dimensions together then you should get a volume of 54 in² then divide by 1/2 to find out how many cubes will fit in the prism

Answer:

Step-by-step explanation:

= factorial of n= real or complex number= nth derivative of f evaluated at the point a

Answer:

Here you go!

Step-by-step explanation:

The answer is a 7.29 dollar tip.

Answer:

The total cost will be $43.74

Step-by-step explanation:

To solve the problem we first have to find what is 20% of $36.45.

To do this, multiply 36.45 by .20

36.45 x .20 = 7.29

now that we know how much is the tip, we add that to the bill

36.45 + 7.29 = 43.74

your final answer will be $43.74

Answer:

30% of the mass of an object is 24 kilograms. Use this fact to find: a 60% of the mass b 10% of the mass c 50% of the mass d the whole mass of the object​

Step-by-step explanation:

However, if the decisions drawn from both methods differ (e.g., one rejects the null hypothesis while the other does not), then the conclusions are not the same.

In order to compare the conclusions obtained using the p-value method with your initial conclusion, it is essential to first understand the p-value's role in hypothesis testing. The p-value is a probability that helps in determining the statistical significance of your test results. A smaller p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, leading to its rejection in favour of the alternative hypothesis. Conversely, a larger p-value (typically > 0.05) suggests weak evidence against the null hypothesis, and therefore, it cannot be rejected.
When comparing the conclusions, assess if both methods lead to the same decision regarding the null hypothesis. If your initial conclusion rejects the null hypothesis and the p-value method yields a p-value ≤ 0.05, then the conclusions are the same. Alternatively, if your initial conclusion does not reject the null hypothesis and the p-value method results in a p-value > 0.05, the conclusions also align.
However, if the decisions drawn from both methods differ (e.g., one rejects the null hypothesis while the other does not), then the conclusions are not the same. In such cases, it is crucial to revisit the methodology and ensure the correctness of the approach taken, as it is vital to have consistent and accurate results in any statistical analysis.

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Answer:

A/c to question

(10-k)/4=2

or, (10-k)=8

or,10-8=k

or, k=2

Thus the value of k is 2.

Thus the value of k is 2.

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

Simplification is to make something easier to do or understand and to make something less complicated.

Given

The difference of 10 and k divided by 4 yields 2.

The value of k

The difference of 10 and k divided by 4 yields 2 can be written mathematically.

\(\rm \dfrac{10-k}{4} = 2\)

Then simplify the equation,

\(\begin{aligned} \rm \dfrac{10-k}{4} &= 2\\\rm 10 - k &= 8\\10 - 8 &= \rm k \\\rm k &= 2 \end{aligned}\)

Thus the value of k is 2.

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Answer: 1/20

Step-by-step explanation:

1/20 liters because 5 times 4/1 (5 divided by 1/4) equals 1/20

Pi is a symbol in mathematics that represents the ratio of the circumference of a circle to its diameter. Its symbol looks like this: π.

The number π is a mathematical constant that is approximately equal to 3.14. It is a non-repeating, non-terminating decimal that has been determined to more than one trillion decimal places. The symbol π (pronounced "pi") represents the ratio of the circumference of a circle to its diameter. The value of π is used in numerous mathematical equations, including those related to circles, spheres, and trigonometry.

Pi is irrational because it is a non-repeating, non-terminating decimal. This means that it cannot be represented as a simple fraction or ratio of two numbers. Pi is an important mathematical constant that is used in a variety of calculations in mathematics and physics, including the calculation of the area and circumference of a circle.

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Answer:

Please refer to the photo

I don't know which one you want

When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

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Answer:

        \(y=\frac{1}{2}x+5\)

Step-by-step explanation:

Considering the line graph

Some of the points on the line are given by

Finding the slop between any two given points

Let us take the point (0, 5) and (2, 6)

\(\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(0,\:5\right),\:\left(x_2,\:y_2\right)=\left(2,\:6\right)\)

\(m=\frac{6-5}{2-0}\)

To the  y-intercept, set x = 0.

We already know that when x = 0, the value of y = 5

so

Equation of line can be obtained using the point-slope form of the line equation

\(y-y_1=m\left(x-x_1\right)\)

substituting the values m = 1/2 and any point let say (2, 6)

\(y-6=\frac{1}{2}\left(x-2\right)\)

add 6 to both sides

\(y-6+6=\frac{1}{2}\left(x-2\right)+6\)

\(y=\frac{1}{2}x+5\)

Therefore, the equation of the line is: